The patent badge is an abbreviated version of the USPTO patent document. The patent badge does contain a link to the full patent document.
The patent badge is an abbreviated version of the USPTO patent document. The patent badge covers the following: Patent number, Date patent was issued, Date patent was filed, Title of the patent, Applicant, Inventor, Assignee, Attorney firm, Primary examiner, Assistant examiner, CPCs, and Abstract. The patent badge does contain a link to the full patent document (in Adobe Acrobat format, aka pdf). To download or print any patent click here.
Patent No.:
Date of Patent:
Feb. 12, 1980
Filed:
Nov. 18, 1977
Daniel Graupe, Fort Collins, CO (US);
Aloysius A Beex, Fort Collins, CO (US);
G Donald Causey, Chevy Chase, MD (US);
Other;
Abstract
A near minimum order ARMA type recursive filter with guaranteed stability and convergence is provided together with a method for obtaining the parameters of such filter. The amplitude/frequency response of the filter approximates an arbitrarily selected frequency spectrum of amplitude, and the phase response approximates a substantially linear function of frequency with an arbitrarily selected slope because the parameters are identified, off-line, using a minimization process that minimizes an integral error norm. The first step involves performing an inverse discrete Fourier transform of the arbitrarily selected frequency spectrum of amplitude to obtain a truncated sequence of coefficients of a stable, pure moving-average filter model, i.e., the parameters of a non-recursive filter model. The truncated sequence of coefficients, which has N+1 terms, is then convolved with a random sequence to obtain an output sequence associated with the random sequence. A time-domain, convergent parameter identification is then performed, in a manner that minimizes an integral error function norm, to obtain the near minimum order parameters .alpha..sub.i and .beta..sub.j of the model having the desired amplitude- and phase-frequency responses, the parameters satisfying the relationship: ##EQU1## where: .alpha..sub.i is the ith auto-regressive parameter, and .beta..sub.j is the jth moving-average parameter, respectively, of an ARMA-type recursive filter; n and m denote the order of the auto-regressive and the moving-average parts of the ARMA model, respectively; y.sub.k and u.sub.k are associated elements of the kth element of the output sequence and the random sequence, respectively; k is an integer; and v is a shift integer selected to provide the desired slope of the phase response given by 2.pi.(v-N/2).